


An Engineering Analysis of a Fire Nation Battleship

by llwydion



Category: Avatar: The Last Airbender
Genre: Gen, it's an engineering analysis, of a fire nation ship, please don't read if you're allergic to math/science, sue me i'm a nerd, this is not a work of literature
Language: English
Status: Completed
Published: 2017-04-12
Updated: 2017-04-12
Packaged: 2018-10-17 22:46:02
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 638
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/10603854
Author URL: https://archiveofourown.org/users/llwydion/pseuds/llwydion
Summary: Weren't you wondering how many firebenders it would take to power a Fire Nation battleship? Well, wonder no longer. llwydion proudly presents a mechanical/chemical engineering analysis of a Fire Nation battleship!No, really. It really is an engineering analysis. Please don't force yourself to read through the work if you don't understand it.





	

**Author's Note:**

> REPEATED WARNING: THIS IS AN ENGINEERING ANALYSIS. PLEASE DON'T FORCE YOURSELF TO READ IT IF YOU DON'T UNDERSTAND IT.
> 
> Derived solely for pleasure, because I am both an engineering nerd and an A:TLA fan. I do apologize for the formatting; I haven't seemed to figure out how to add LaTex'ed equations without having to upload them somewhere.

**The question:** How many firebenders would you need to power a Fire Nation battleship? (also includes an analysis for coal, just for comparison) We're talking a typical, A:TLA size battleship, not the later LOK ones.

 **Modeling:** The battleship can be approximated as about 210 m in length, 30 m in width, with an unknown height. Even better, on [this](https://forums.spacebattles.com/threads/fire-nation-navy-ships-vs-real-world-ironclads.248637/) forum I found, someone suggested that these battleships can be approximated as [Iowa-class battleships](https://en.wikipedia.org/wiki/Iowa-class_battleship), which is what I'm using here, only scaled up. I'm assuming the heights of the Fire Nation and Iowa-class battleships are the same.

 **System:** open, the individual processes used to power the ship

**Assumptions:**

\- the ship is already ballasted to be neutrally buoyant (in non-arcane speak, that means it won't sink)

\- ship operates on a real Rankine cycle with [these](http://www.powerengineeringint.com/articles/print/volume-20/issue-4/features/pushing-the-steam-cycle-boundaries.html) current industrial limits

\- operating at steady-state

\- isobaric (same pressure in and out) boiler and condenser

\- incompressible liquid flows into the pump

\- working fluid in the cycle is water

\- the ship is being powered separately from how much work it's putting out

 

First, I need to figure out how much power is needed to propel this forward. An Iowa-class battleship (henceforth abbreviated as "Iowa") needs 158000 kW of power. If we scale this with respect to the difference between the two volumes,

(270 m * 33 m * height)/158000 kW = (210 m * 30 m * height)/power

or power = 120000 kW (approximately)

Next, we have a real Rankine cycle where the pressure of the fluid going into the boiler (state 2) is about 20 MPa. I really wish I could attach an image here, since that would make picturing things much easier, but here's a few pictures of a Rankine cycle (I didn't draw this! [here's](http://www.powerfromthesun.net/Book/chapter12/chapter12.html) the link) to help. The temperature of state 3 was 550 degrees C, and the pressure of state 4 was 3 kPa, assuming seawater cooling.

Now, we look at the physical laws involved in this process. The picture below, taken from [here](http://machineryequipmentonline.com/hydraulics-and-pneumatics/wp-content/uploads/2016/03/POWER-AND-REFRIGERATION-CYCLES-0336_thumb.jpg), is for an ideal Rankine cycle; the real one also takes into account the [isentropic efficiencies](https://en.wikipedia.org/wiki/Thermal_efficiency#Overview) of the [turbine](http://www.massengineers.com/Documents/isentropic_efficiency.htm) and [pump.](http://www.ecourses.ou.edu/cgi-bin/ebook.cgi?topic=th&chap_sec=06.5&page=theory)

For this case, I assumed a turbine efficiency of 0.9 (which is a good turbine), and a pump efficiency of 0.9 (which is really good).

Since I realize this is for a highly technical audience and I don't want to bore you all, pretty much we go through, look up some values in thermodynamic tables and do some calculations, and end up with these values:

h1 = hf = 100.98 kJ/kg

v1 = vf = 0.001003 m^3/kg

h2s = 121.04 kJ/kg (the 2s indicates that it's the isentropic version of state 2)

h2 = 123.27 kJ/kg

h3 = 3396.2 kJ/kg

s3 = 6.3390 kJ/kgK (this is used to find the values for 4s)

x4s = 0.73 (quality of state 4s)

h4s = 1879.82 kJ/kg

h4 = 2031.46 kJ/kg

Now, for the number of firebenders! If we assume one bender outputs the same amount as a 1.44 kW space heater, we'd need about 120000 kW/1.44 kW/bender = 83334 benders.

The ship probably can't keep that many benders on board (are there even that many benders in the Fire Nation?), so coal is probably their fuel of choice.

If we use coal instead,

heating value of coal: 33000 kJ/kg

We assume that about 80% of the heat from coal goes into the water in the boiler. So, using some more calculations, we need about 39.92 metric tons of coal per hour.

 

In other words, there is no way these ships are moving on a Rankine cycle, using firebenders or using coal. Thus ends the analysis (mainly because I'm currently taking an intro chem engineering class and really haven't talked much beyond the Carnot and Rankine cycles...)


End file.
